Inkjet printing technology for solar cell metallization is considered as an important alternative with inherent non-contact characteristics. The melting process of silver particles plays the key role which determines the final structure of finger electrodes. To explore the melting of silver particles inside the silicon wafers, an enthalpy-based LB-FD model is presented to simulate the solid-liquid phase transitions in the multiphase system. In vertical thermal fields, silver particles melt from bottom to upper layers. The adhesion and coalescence behaviors of multiple particles are well captured in multiphase melting. The melting fluids near the sidewall are simulated with the interfacial tension and gravitational force. The effects of solid phase ratio and textured features of silicon wafers are also studied. The presented 3D enthalpy-based LB-FD model exhibits powerful capacities to solve the solid-liquid phase transitions in multiphase system. The numerical analysis provides a better insight to understand and improve the inkjet-printed solar cell metallization process.